jee-main

Papers (169)
2025
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2024
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2023
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2022
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2021
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2020
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2019
session1_09jan_shift1 6 session1_09jan_shift2 29 session1_10jan_shift1 30 session1_10jan_shift2 12 session1_11jan_shift1 6 session1_11jan_shift2 5 session1_12jan_shift1 10 session1_12jan_shift2 20 session2_08apr_shift1 29 session2_08apr_shift2 29 session2_09apr_shift1 29 session2_09apr_shift2 29 session2_10apr_shift1 2 session2_10apr_shift2 3 session2_12apr_shift1 3 session2_12apr_shift2 9
2018
08apr 29 15apr 28 15apr_shift1 28 15apr_shift2 2 16apr 15
2017
02apr 28 08apr 29 09apr 30
2016
03apr 30 09apr 30 10apr 28
2015
04apr 29 10apr 30
2014
06apr 28 09apr 28 11apr 4 12apr 5 19apr 29
2013
07apr 29 09apr 14 22apr 5 23apr 14 25apr 13
2012
07may 18 12may 22 19may 13 26may 17 offline 30
2011
jee-main_2011.pdf 13
2010
jee-main_2010.pdf 1
2009
jee-main_2009.pdf 1
2008
jee-main_2008.pdf 1
2007
jee-main_2007.pdf 38
2005
jee-main_2005.pdf 19
2004
jee-main_2004.pdf 11
2003
jee-main_2003.pdf 9
2002
jee-main_2002.pdf 8
2018 16apr

15 maths questions

Q61 Solving quadratics and applications Finding roots or coefficients of a quadratic using Vieta's relations View
Let $p , q$ and $r$ be real numbers ( $p \neq q , r \neq 0$ ), such that the roots of the equation $\frac { 1 } { x + p } + \frac { 1 } { x + q } = \frac { 1 } { r }$ are equal in magnitude but opposite in sign, then the sum of squares of these roots is equal to
(1) $p ^ { 2 } + q ^ { 2 }$
(2) $\frac { p ^ { 2 } + q ^ { 2 } } { 2 }$
(3) $2 \left( p ^ { 2 } + q ^ { 2 } \right)$
(4) $p ^ { 2 } + q ^ { 2 } + r ^ { 2 }$
Q62 Reciprocal Trig & Identities View
If an angle $A$ of a $\triangle A B C$ satisfies $5 \cos A + 3 = 0$, then the roots of the quadratic equation $9 x ^ { 2 } + 27 x + 20 = 0$ are
(1) $\sec A , \cot A$
(2) $\sec A , \tan A$
(3) $\tan A , \cos A$
(4) $\sin A , \sec A$
Q63 Complex Numbers Arithmetic Trigonometric/Polar Form and De Moivre's Theorem View
The least positive integer $n$ for which $\left( \frac { 1 + i \sqrt { 3 } } { 1 - i \sqrt { 3 } } \right) ^ { n } = 1$ is
(1) 2
(2) 5
(3) 6
(4) 3
Q64 Permutations & Arrangements Forming Numbers with Digit Constraints View
The number of numbers between 2,000 and 5,000 that can be formed with the digits $0,1,2,3,4$ (repetition of digits is not allowed) and are multiple of 3 is
(1) 36
(2) 30
(3) 24
(4) 48
Q65 Arithmetic Sequences and Series Telescoping or Non-Standard Summation Involving an AP View
Let $\frac { 1 } { x _ { 1 } } , \frac { 1 } { x _ { 2 } } , \ldots , \frac { 1 } { x _ { n } } \left( x _ { i } \neq 0 \right.$ for $\left. i = 1,2 , \ldots , n \right)$ be in A.P. such that $x _ { 1 } = 4$ and $x _ { 21 } = 20$. If $n$ is the least positive integer for which $x _ { n } > 50$, then $\sum _ { i = 1 } ^ { n } \left( \frac { 1 } { x _ { i } } \right)$ is equal to
(1) 3
(2) $\frac { 1 } { 8 }$
(3) $\frac { 13 } { 4 }$
(4) $\frac { 13 } { 8 }$
Q66 Geometric Sequences and Series Finite Geometric Sum and Term Relationships View
The sum of the first 20 terms of the series $1 + \frac { 3 } { 2 } + \frac { 7 } { 4 } + \frac { 15 } { 8 } + \frac { 31 } { 16 } + \ldots$ is
(1) $39 + \frac { 1 } { 2 ^ { 19 } }$
(2) $38 + \frac { 1 } { 2 ^ { 20 } }$
(3) $38 + \frac { 1 } { 2 ^ { 19 } }$
(4) $39 + \frac { 1 } { 2 ^ { 20 } }$
Q67 Binomial Theorem (positive integer n) Find a Specific Coefficient in a Product of Binomial/Polynomial Expressions View
The coefficient of $x ^ { 2 }$ in the expansion of the product $\left( 2 - x ^ { 2 } \right) \left\{ \left( 1 + 2 x + 3 x ^ { 2 } \right) ^ { 6 } + \left( 1 - 4 x ^ { 2 } \right) ^ { 6 } \right\}$ is
(1) 107
(2) 108
(3) 155
(4) 106
Q68 Conic sections Locus and Trajectory Derivation View
The locus of the point of intersection of the lines $\sqrt { 2 } x - y + 4 \sqrt { 2 } k = 0$ and $\sqrt { 2 } k x + k y - 4 \sqrt { 2 } = 0$ ( $k$ is any non-zero real parameter) is
(1) an ellipse whose eccentricity is $\frac { 1 } { \sqrt { 3 } }$
(2) a hyperbola whose eccentricity is $\sqrt { 3 }$
(3) a hyperbola with length of its transverse axis $8 \sqrt { 2 }$
(4) an ellipse with length of its major axis $8 \sqrt { 2 }$
Q69 Circles Circles Tangent to Each Other or to Axes View
If a circle $C$, whose radius is 3 , touches externally the circle $x ^ { 2 } + y ^ { 2 } + 2 x - 4 y - 4 = 0$ at the point $( 2,2 )$, then the length of the intercept cut by this circle $C$ on the $x$-axis is equal to
(1) $2 \sqrt { 3 }$
(2) $\sqrt { 5 }$
(3) $3 \sqrt { 2 }$
(4) $2 \sqrt { 5 }$
Q70 Conic sections Optimization on Conics View
Let $P$ be a point on the parabola $x ^ { 2 } = 4 y$. If the distance of $P$ from the center of the circle $x ^ { 2 } + y ^ { 2 } + 6 x + 8 = 0$ is minimum, then the equation of the tangent to the parabola at $P$ is
(1) $x + y + 1 = 0$
(2) $x + 4 y - 2 = 0$
(3) $x + 2 y = 0$
(4) $x - y + 3 = 0$
Q71 Conic sections Eccentricity or Asymptote Computation View
If the length of the latus rectum of an ellipse is 4 units and the distance between a focus and its nearest vertex on the major axis is $\frac { 3 } { 2 }$ units, then its eccentricity is
(1) $\frac { 2 } { 3 }$
(2) $\frac { 1 } { 2 }$
(3) $\frac { 1 } { 9 }$
(4) $\frac { 1 } { 3 }$
Q72 Chain Rule Limit Evaluation Involving Composition or Substitution View
$\lim _ { x \rightarrow 0 } \frac { ( 27 + x ) ^ { \frac { 1 } { 3 } } - 3 } { 9 - ( 27 + x ) ^ { \frac { 2 } { 3 } } }$ equals
(1) $- \frac { 1 } { 6 }$
(2) $\frac { 1 } { 6 }$
(3) $\frac { 1 } { 3 }$
(4) $- \frac { 1 } { 3 }$
Q73 Proof True/False Justification View
If $p \rightarrow ( \sim p \vee \sim q )$ is false, then the truth values of $p$ and $q$ are, respectively
(1) $F , F$
(2) $T , T$
(3) $F , T$
(4) $T , F$
Q74 Measures of Location and Spread View
The mean and the standard deviation (S. D.) of five observations are 9 and 0 , respectively. If one of the observation is increased such that the mean of the new set of five observations becomes 10 , then their S. D. is
(1) 0
(2) 2
(3) 4
(4) 1
Q75 Sine and Cosine Rules Heights and distances / angle of elevation problem View
A man on the top of a vertical tower observes a car moving at a uniform speed towards the tower on a horizontal road. If it takes 18 min for the angle of depression of the car to change from $30 ^ { \circ }$ to $45 ^ { \circ }$, then the time taken (in $\min$ ) by the car to reach the foot of the tower is
(1) $\frac { 9 } { 2 } ( \sqrt { 3 } + 1 )$
(2) $9 ( \sqrt { 3 } + 1 )$
(3) $18 ( \sqrt { 3 } - 1 )$
(4) $9 ( \sqrt { 3 } - 1 )$